Please read my articles below and to the left, if you want to learn some strategies as your son or daughter prepares for the SAT. Clearly, one fact emerges that the students who demonstrate by their SAT scores that they are college ready are those who take advanced courses in high school – Trigonometry, Calculus, and Pre-Calculus along with Honors or AP classes.

I would add, based upon current research such as cited by Van de Walle, Kamp, and Bay-Williams (2013), that U.S. mathematics scores have been traditionally lower than those in some Asian countries (most notably Singapore), due to the continued emphasis on procedural skills, without much deep understanding of content. In the United States, we have mostly been taught procedural mathematics, with little emphasis on the underlying conceptual knowledge. Thus, students learn how to make computations with little understanding of how to utilize these skills in real world mathematics. The landmark mathematics treatise, “Adding It Up” (National Research Council, 2001), stated that, as in anything, there needs to be a balance between conceptual knowledge and procedural fluency. Otherwise, students will be able to mimic the sample problem the teacher places on the board and dutifully solve more problems of the same type that day; but, overall, they tend to have difficulty at a later date ascertaining when to utilize the procedure taught when solving real world problems. More evidence that our current state of mathematics instruction based upon procedural knowledge alone does not benefit our citizens is the fact that many adults state, almost proudly, “I never did understand math,” or “Math was always hard for me.”

I have begun to offer Pre-Algebra lessons in addition to reading and writing remediation and ESL instruction. The classes (usually with three students) will begin with a mathematics problem, but I will not provide a formula to help in solving the problem. I will help remind students of what they already know and give them mathematical manipulatives to use as well as provide tips and hints on a means of solving the problem. An example of such a problem would be to provide students with cut-outs of right triangles and graph paper before students have learned the Pythagorean Theorem and have students use their prior knowledge of how to find the area of a rectangle to help them figure out the formula for solving right triangles (I urge you to try this at home! It is easy to see that the right triangle is one half of the area of a rectangle, making it easy to see why you multiply the 1/2 times the base times the height, because the base and the height of the right triangle are simply the length and width of the rectangle).

After the students have come up with a solution to the problem, we will have a discussion about the problem and how they solved it and look at other problems to see if the “solution” they discovered will work for other problems. I have students take notes about their problem solution and maintain a mathematical notes folder that contains words, images, and symbols to help them remember their solution. Then, I will have the student solve more problems of this type, in order to gain the procedural fluency that they need to solve mathematical problems quickly and efficiently.

The manipulatives we use will include cut-outs, graph paper, and vitual manipulatives that they will have access to whenever they would like to use them. Note: In addition to the cut-out manipulatives, the virtual manipulatives I now use are online. I am in the process of finding the iOS and Android virtual mathematics manipulatives that can be downloaded, so a student can utilize them even when they do not have Internet access.

Finally, the Atlantic article about the 2013 SAT scores did not break down the scores by SAT category, but I would also remind parents that a key determining factor in reading success is wide reading. Has your child always picked up a wide range of books, reading daily and consistently? If so, and especially if they are taking advanced courses in high school, they are likely to be poised to receive a high score on the SAT Critical Reading and Vocabulary sections, because they will have a far greater vocabulary than their peers who are not wide readers. Please see my articles on the SAT Reading and Writing Preparation to the left (or below), if you would like to find out more.

If you are interested in scheduling an appointment for an online reading or writing remediation, SAT preparation, Pre-Algebra, or ESL lesson, please see this link for information: